mathematician

Information about mathematician

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Leonhard Euler, considered one of the greatest mathematicians of all time


A mathematician is a person whose primary area of study and research is the field of mathematics.

Problems in mathematics

Some people incorrectly believe that mathematics has been fully understood, but the publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals. One of the most exciting recent developments was the proof of Fermat's last theorem, following 350 years of the brightest mathematical minds attempting to settle the problem.

There are many famous open problems in mathematics, many dating back tens, if not hundreds, of years. Some examples include the Riemann hypothesis (from 1859) and Goldbach's conjecture (1742). The Millennium Prize Problems highlight longstanding, famous problems in mathematics and offers a US$1,000,000 reward for solving any one of them. One of these problems, the Poincaré conjecture (1904), was proven by Russian mathematician Grigori Perelman in a paper released in 2003; peer review was completed in 2006, and the proof was accepted as valid. [1]

Motivation

Mathematicians are typically interested not in calculating, but in finding and describing patterns, or creating proofs that justify a theorem mathematically. Problems have come from physics, economics, games, computer science and generalizations of earlier mathematics. Some problems are simply created for the challenge of solving them. Although much mathematics is not immediately useful, history has shown that eventually applications are found. For example, number theory originally seemed to be without purpose to the real world, but after the development of computers it gained important applications to algorithms and cryptography.

There are no Nobel Prizes awarded to mathematicians. The award that is generally viewed as having the highest prestige in mathematics is the Fields Medal. This medal, sometimes described as the "Nobel Prize of Mathematics", is awarded once every four years to as many as four young (under 40 years old) awardees at a time. Other prominent prizes include the Abel Prize, the Nemmers Prize, the Wolf Prize, the Schock Prize, and the Nevanlinna Prize.

Differences

Mathematicians differ from scientists in that physical theories in the sciences are usually assumed to be an approximation of truth, while mathematical statements are an attempt at capturing truth. If a certain statement is believed to be true by mathematicians (typically because special cases have been confirmed to some degree) but has neither been proven nor disproven to logically follow from some set of assumptions, it is called a conjecture, as opposed to the ultimate goal: a theorem that is proven true. Physical theories may be expected to change whenever new information about our physical world is discovered. Mathematics changes in a different way: new ideas don't falsify old ones but rather are used to generalize what was known before to capture a broader range of phenomena. For instance, calculus (in one variable) generalizes to multivariable calculus, which generalizes to analysis on manifolds. The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint without making what was proved before in any way incorrect. While a theorem, once proved, is true forever, our understanding of what the theorem really means gains in profundity as the mathematics around the theorem grows. A mathematician feels that a theorem is better understood when it can be extended to apply in a broader setting than previously known. For instance, Fermat's little theorem for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.

Demographics

While the majority of mathematicians are male, there have been some demographic changes since World War II. Some prominent female mathematicians are Emmy Noether (1882 - 1935), Sophie Germain (1776 - 1831), Sofia Kovalevskaya (1850 - 1891), Rózsa Péter (1905 - 1977), Julia Robinson (1919 - 1985), Mary Ellen Rudin, Eva Tardos, Émilie du Châtelet, Mary Cartwright, Hypatia of Alexandria, Marianna Csörnyei, Ingrid Daubechies and Nicole El Karoui. The AMS and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

Doctoral degree statistics for mathematicians in the United States

The number of doctoral degrees in mathematics awarded each year in the United States has ranged from 750 to 1230 over the past 35 years. In the early seventies, degree awards were at their peak, followed by a decline throughout the seventies, a rise through the eighties, and another peak through the nineties. Unemployment for new doctoral recipients peaked at 10.7% in 1994 but was as low as 3.3% by 2000. The percentage of female doctoral recipients increased from 15% in 1980 to 30% in 2000.

As of 2000, there are approximately 21,000 full-time faculty positions in mathematics at colleges and universities in the United States. Of these positions about 36% are at institutions whose highest degree granted in mathematics is a bachelor's degree, 23% at institutions that offer a master's degree and 41% at institutions offering a doctoral degree.

The median age for doctoral recipients in 1999-2000 was 30, and the mean age was 31.7.

Quotations

The following are quotations about mathematicians, or by mathematicians.

A mathematician is a machine for turning coffee into theorems.
:—Attributed to both Alfréd Rényi [2] and Paul Erdős


Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. (Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)
:—Johann Wolfgang von Goethe


Some humans are mathematicians; others aren't.
:—Jane Goodall (1971) In the Shadow of Man


Each generation has its few great mathematicians...and [the others'] research harms no one.
:—Alfred Adler, "Mathematics and Creativity"[1]


Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
:—Bertrand Russell, The Study of Mathematics


Another roof, another proof.
:—Paul Erdős


Some of you may have met mathematicians and wondered how they got that way.
:—Tom Lehrer

See also

Notes

1. ^ Alfred Adler, "Mathematics and Creativity," The New Yorker, 1972, reprinted in Timothy Ferris, ed., The World Treasury of Physics, Astronomy, and Mathematics, Back Bay Books, reprint, June 30, 1993, p, 435.

References

  • A Mathematician's Apology, by G. H. Hardy. Memoir, with foreword by C. P. Snow.
  • Reprint edition, Cambridge University Press, 1992; ISBN 0-521-42706-1
  • First edition, 1940
  • Dunham, William. The Mathematical Universe. John Wiley 1994.
  • Paul Halmos. I Want to Be a Mathematician. Springer-Verlag 1985.

External links

Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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scientific journal is a publication intended to further the progress of science, usually by reporting new research. Most journals are highly specialized, although some of the oldest journals such as Nature
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In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. A proof is a logical argument, not an empirical one. That is, one must demonstrate that a proposition is true in all cases before it is considered a theorem of mathematics.
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Fermat's last theorem states that:

It is impossible to separate any power higher than the second into two like powers,


or, more precisely:


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Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics.
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Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics.[1] It states:

Every even integer greater than 2 can be written as the sum of two primes.

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The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved. A correct solution to each problem results in a $1,000,000 prize (sometimes called a Millennium Prize
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United States dollar
dólar estadounidense (Spanish)
dólar amerikanu (Tetum)
dólar americano
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In mathematics, the Poincaré conjecture (IPA: [pwɛ̃kaˈʁe])[1] is a theorem about the characterization of the three-dimensional sphere amongst three-dimensional manifolds.
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Grigori Yakovlevich Perelman
Born May 13 1966 (1966--) (age 41)
Leningrad, USSR
Field Mathematician
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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game is a structured or semi-structured , usually undertaken for enjoyment and sometimes also used as an educational tool. (The term "game" is also used to describe simulation of various activities e.g., for the purposes of training, analysis or prediction, etc.
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Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems.
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Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
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Cryptography (or cryptology; derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write" or λεγειν legein
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The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years.
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The Abel Prize is presented annually by the King of Norway to outstanding mathematicians. In 2001 the government of Norway announced that the bicentennial of Norwegian mathematician Niels Henrik Abel's birth (which was 1802) would mark the commencement of a new prize for
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The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, part of a $14 million donation from the Nemmers brothers.
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The Wolf Prize has been awarded annually since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among peoples ... irrespective of nationality, race, colour, religion, sex or political views.
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The Rolf Schock Prizes were established and endowed by bequeath of philosopher and artist Rolf Schock (1933-1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and have been awarded every two years since. Each recipient currently receives SEK400,000 (ca.
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The Rolf Nevanlinna Prize is awarded once every 4 years at the International Congress of Mathematicians, for outstanding contributions in Mathematical Aspects of Information Sciences including:

1.
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An approximation is an inexact representation of something that is still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.
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In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic.
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Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series, and constitutes a major part of modern university education.
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Multivariable calculus is the extension of calculus in one variable to calculus in several variables: the functions which are differentiated and integrated involve several variables rather than one variable.
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manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension is important.
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Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problematics of geometry.
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